A possible deformed algebra and calculus inspired in nonextensive thermostatistics
Ernesto P. Borges (Universidade Federal da Bahia, Salvador-BA, Brazil)
TL;DR
This paper introduces a deformed algebra, q-derivative, and q-integral inspired by nonextensive thermostatistics, providing new mathematical tools with potential applications in statistical mechanics.
Contribution
It develops a novel deformed algebra and calculus based on q-exponential and q-logarithm functions, expanding mathematical frameworks in nonextensive statistical mechanics.
Findings
Defined a q-derivative with q-exponential as eigenfunction
Established a dual nature between q-derivative and q-integral
Provided a consistent mathematical structure for nonextensive calculus
Abstract
We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an eigenfunction. The q-derivative and the q-integral have a dual nature, that is also presented.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.